Year: 2026
Type: preprint
Abstract: We compute the scaling dimensions of monopole operators in QED$_3$ with $N$ 2-component complex fermions and Chern-Simons level $k$ to subleading order in the limit where $k,N$ are large and $k/N$ is fixed, which generalizes previous results for scalar QED$_3$ (sQED$_3$) coupled to $N$ complex scalars. In both cases, at leading large $N$ many monopole operators are degenerate, and we compute their energy splitting. We use these results to check the duality between QED$_3$ with $N=1,k=-3/2$ and sQED$_3$ with $N=1,k=2$, whose $U(1)$ monopole symmetry is enhanced to $SO(3)$. We find the scaling dimensions in each dual theory match to high precision for all charges, the lowest charge spin 1 monopoles are close to 2 as expected for the emergent $SO(3)$ current, and the degenerate second lowest charge monopoles match a prediction from a fuzzy sphere calculation, including the energy splitting. We also find similar evidence for dualities between QED$_3$ with $N=1,k=-(2m+1)/2$ and one scalar coupled to two $U(1)$ gauge fields, which has an effective description as sQED$_3$ with $N=1,k=\frac{m+1}{m}$ and $q_s=mq_f$ for $m>1$. Finally, we also find similar evidence for Son's duality between QED$_3$ with $N=1,k=0$ and a free fermion, and clarify a previously discussed match between sQED$_3$ with $N=k=1$ dual to a free fermion.
Source: arXiv (Cornell University)
Authors: Chester, Shai M., Dupuis, Éric
Institutions: Imperial College London, Université de Montréal
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Imperial College London
Award: G4591806611
OpenAlex ID: W7214925131